Moving from CVS to git: $Id:$ equivalent?

I read through a bunch of questions asking about simple source code control tools and git seemed like a reasonable choice. I have it up and running and it works well so far. One aspect that I like about CVS is the automatic incrementation of a version number.

I understand that this makes less sense in a distributed repository, but as a developer I want/need something like this. Let me explain why:

I use Emacs. Periodically I go through and look for new versions of the lisp source files for 3rd-party packages. Say I've got a file foo.el which according to the header is version 1.3; if I look up the latest version and see it's 1.143 or 2.6 or whatever, I know I'm pretty far behind. If instead I see a couple of 40-character hashes, I won't know which is later or get any idea of how much later it is. I would absolutely hate it if I had to manually check ChangeLogs just to get an idea of how out of date I am.

As a developer, I want to extend this courtesy, as I see it, to the people that use my output (and maybe I'm kidding myself that anyone is, but let's leave that aside for a moment). I don't want to have to remember to increment the damn number myself every time, or a timestamp or something like that. That's a real PITA, and I know that from experience.

So what alternatives do I have? If I can't get an $Id:$ equivalent, how else can I provide what I'm looking for? Thanks for the help!

EDIT: I should mention that my expectation is that the end user will NOT have git installed and even if they do, will not have a local repository (indeed, I expect not to make it available that way). Thanks for the answers so far!

Let's say, for example, you packaged a version file with the source (or even rewrote all the content for distribution) to show that number. Let's say that packaged version was 2.2-12-g6c4ae7a (not a release, but a valid version).

You can now see exactly how far behind you are (4 commits), and you can see exactly which 4 commits:

# The RHS of the .. can be origin/master or empty, or whatever you want.
% git log --pretty=format:"%h %an %s" 2.2-12-g6c4ae7a..2.2-16-gc0cd61a
c0cd61a Dustin Sallings More tries to get a timeout.
8c489ff Dustin Sallings Made the timeout test run on every protocol on every bui
fb326d5 Dustin Sallings Added a test for bug 35.
fba04e9 Valeri Felberg Support passing an expiration date into CAS operations.